I've always heard the bigger the breed, the sweeter the dog. I've got two Jack Russell Terriers and they're the most nervous, snappy dogs I've ever owned. I imagine a German Shepard would get along fine with your shih-tzu,
IF your
shih-tzu allows it.
The shelter should have some information on the dogs temperament, because like Tserisa said, most dogs have to go through several temperament tests before being deemed "adoptable".